When should a percentage be written as a percentage and when should it be written x out of n?@Josh based on your comment I believe my first comment still holds true. I'm not sure what relevance it has on the question which is the last sentence in my original post. If you want to get hung up on my use of the word better than I can edit it out. "I'm looking for research on how people perceive actual percentages vs n out of x." Now, if I'm missing something and you believe there is a fundamental difference in the answer if the word better is left in vs removed please comment. Otherwise I'm still not sure what difference any of this makes on the question.

Aug13

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When should a percentage be written as a percentage and when should it be written x out of n?@Josh What difference would it make? Its kinda like you're saying you can't explain how people perceive relative speed / motion without knowing if the objective is to feel fast or feel slow. If you understand how people perceive motion you should be able to make something appear fast or slow. I'm looking for a similar understanding regarding how people perceive percentages.